Effects of Damage Field on Elastic Stress Singularity at a Mode III Crack

The effects of damage field on the stress singularity at a crack tip are investigated. For a radial damage distribution represented by a power function γm of radius γ with its center at the crack-tip, an analytical solution of asymptotic elastic stress fields is obtained for a mode III crack. The asymptotic distribution of the stress field is found to depend on the power law index m of the given damage distribution, and the well known elastic singularity disappears when the power law index m of the distribution exceeds a value of 3/4. For more general damage distributions, numerical analyses by means of the finite element method were performed, and the effects of the geometry shape of two local damage fields on the stress distribution around the crack were elucidated. It was shown that, though the preceding damage field behind the crack-tip significantly influences the stress field in front of a growing crack, the analytical solution for the circular damage field gives essentially the same stress singularity as that for more general damage distribution. The results provide important insights into some fundamental aspects of the local approach to fracture based on continuum damage mechanics.